If (x -4) is a factor of x^3 ax^2 2bx - 24 and a - b = 8, find the values of a and b.
Answers
Answered by
11
put x=4 in the equation then the equation is form by considering 1 and a-b=8 as2. by using elimination method you find the answer
Answered by
57
x-4=0
=> x=4
f(x)=x³+ax²+2bx-24
f(4)=4³+a.4²+2.b.4-24=0
=>64+16a+8b=24
=> 16a+8b=24-64
=> 2a+1b=3-8
=> 2a+b=-5.........(i)
a-b=8..........(ii)
Solving eq.(i) & (ii)
2a+b=-5
a-b=8
_________
3a=3
=>a=1
Substituting the value of a in eq.(ii)
1-b=8
=>b=-7
That's it! Hope it helps
=> x=4
f(x)=x³+ax²+2bx-24
f(4)=4³+a.4²+2.b.4-24=0
=>64+16a+8b=24
=> 16a+8b=24-64
=> 2a+1b=3-8
=> 2a+b=-5.........(i)
a-b=8..........(ii)
Solving eq.(i) & (ii)
2a+b=-5
a-b=8
_________
3a=3
=>a=1
Substituting the value of a in eq.(ii)
1-b=8
=>b=-7
That's it! Hope it helps
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